Infinite primitive and distance transitive directed graphs of finite out-valency

Amato, Daniela and Evans, David M. (2015) Infinite primitive and distance transitive directed graphs of finite out-valency. Journal of Combinatorial Theory, Series B, 114. pp. 33-50. ISSN 0095-8956

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Abstract

We give certain properties which are satisfied by the descendant set of a vertex in an infinite, primitive, distance transitive digraph of finite out-valency and provide a strong structure theory for digraphs satisfying these properties. In particular, we show that there are only countably many possibilities for the isomorphism type of such a descendant set, thereby confirming a conjecture of the first Author. As a partial converse, we show that certain related conditions on a countable digraph are sufficient for it to occur as the descendant set of a primitive, distance transitive digraph.

Item Type: Article
Uncontrolled Keywords: infinite digraphs,distance transitivity,high arc transitivity,primitive groups
Faculty \ School: Faculty of Science > School of Mathematics
Depositing User: Pure Connector
Date Deposited: 24 Jul 2015 22:35
Last Modified: 22 Apr 2020 00:11
URI: https://ueaeprints.uea.ac.uk/id/eprint/53609
DOI: 10.1016/j.jctb.2015.03.003

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